Definition: An angle bisector is a ray that divides an angle into two equal parts.

Highlight: The angle bisector theorem states that any point on an angle bisector is equidistant from the sides of the angle.

Example: Problem 8 shows solving for x using the equation 4x+30=9x-5, yielding x=7.

Quote: "If a point is on the interior of an angle and equidistant from the sides of the angle, then the point is on the angle bisector."

Definition: A perpendicular bisector is a line that intersects a segment at a 90-degree angle and divides it into two equal parts.

Highlight: The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from the endpoints of the segment it bisects.

Example: Problem 1 demonstrates finding x using the equation 13x-48=7x+24, resulting in x=12 through algebraic manipulation.

Vocabulary: Equidistant means having equal distances from a given point or line.